One-for-one period policy in a two-echelon inventory system with common cycle and Poisson demand rate for retailers

This paper deals with a two-echelon inventory system consisting of one supplier and N retailers. Each retailer faces an independent Poisson demand with the same rate and applies a new ordering policy called one-for-one-period ordering policy for its inventory control. In this ordering policy the order size is equal to one and the time interval between any two consecutive orders forms a common fixed cycle. Thus, the supplier faces a deterministic demand and adopts a deterministic inventory policy. At each cycle he orders a batch of size N to his own supplier. Upon receipt of each batch he sends 1 unit of the product to each retailer with a transportation cost. In this paper, for the above system we first derive the total cost function per unit time. Further, we obtain the conditions under which the total cost function is convex. Finally, we obtain the optimal time interval between any two consecutive orders as well as the optimal average inventory for each retailer.